Human Power Vehicles - 1 (Program: "hpv")

This exercise is the first of a sequence of six programming exercises based on a common theme (which we will develop and evolve throughout the rest of the quarter) in which we wish to evaluate the performance of human powered vehicles (hpv) for land transportation. Performance refers to the steady state velocity reached versus applied human power under constant specific conditions.

Background

Human powered vehicles have captured the imagination of designers, builders, and riders all over the world, for transportation, load carrying, socializing, racing, and touring. My favorite hpv link is the International Human Powered Vehicle Association site which gives one a glimps into hpv activity throughout the world. A more general directory of cycling related websites is presented in Cycling Resources.

In 1992, the 200m world human powered land speed record was set by team Cheetah at 68.73mph. This record was broken by Canadian Sam Whittingham during the 2002 Human Powered Speed Championships in Battle Mountain, Nevada at 81.00mph! During the same event in 2002, Sam's wife, Andrea Blasecki, broke the women's human powered land speed record at 64.74mph. This remarkable husband and wife team from Victoria BC were both riding human powered vehicles built by Canadian sculptor/designer George Georgiev - Sam rode a Varna Diablo II and Andrea a Varna Mephisto, as shown below.

In the 2004 World Human Power Speed Challenge the women's land speed record was broken by Ellen van Vugt from Holland, who did the flying 200m run at 65.89mph! (see below)
 
Ellen van Vugth showing her paces in the Varnowski bike. (Photo by Ruben Garcia from the Pictures of the 2004 WHPSC)
 
Ellen van Vugt was jammed into the bike like a sardine. The bottom bracket was too close and her helmet was jammed into the canopy. (Photo by Brad Teubner from the Pictures of the 2004 WHPSC)

This record was subsequently broken in 2005 by Lisa Vetterlein riding in a Varna at 66.58 mph!

Latest Update (June 2011) In 2009, SamWhittingham broke his own record again for a human powered speed record of 82.819 mph, and Barbara Buatois broke the previous woman's speed record by 9 mph with a speed of 75.458 mph. She subsequently broke her own record in 2010 with a speed of 75.69 mph (refer to the 2011 World Human Power Speed Challenge history of previous events). Barbara Buatois has her own web site with some delightful video's of her record rides.

Human powered vehicles range in complexity from amateur homebuilt machines to exotic machines suitable for commuting or touring, such as the Danish Leitra shown below. The Leitra is an efficient, all weather machine, which includes a hand powered windshield wiper, a rear view mirror conveniently placed above your head, and a well designed ventilated cover which can be lifted on its hinge in a matter of seconds for easy entry or exit.

Typical of the amateur homebuilt machines is the front-wheel-drive Grasshopper I, as shown below: In this picture we see a famous racing rider in his finest hour - racing in the 1993 British Human Power Speed Championships (unfortunately he came last in this race). This was the precurser to the famous Grasshopper series of hpvs, of which the current version is Grasshopper 5.

I have a soft spot for front-wheel-drive human powered vehicles. They result in extremely compact and elegant designs, such as the beautiful Dutch Chinkara or the compact rear-wheel steered construction by Hans Ulrich Reimer. Notice the full suspension on both of these bikes. Another example of a very fast, compact design is the twisting chain front-wheel-drive bike by John Tetz. This is amateur building at its prime - John built both the bike and the fairing.

The Steady State Power Equation

In this first exercise we develop and test the basic power function which we will use without change throughout the exercise sequence.

We first develop the power equation and examine the limitations of the human engine. The word statement of the basic power equation follows:

Recall that the kinetic energy of a mass m moving with velocity V is given by:

The inertial power is given by the time derivative of the kinetic energy, thus:

Thus the complete power equation is given by:

Note that the above equation is a nonlinear differential equation in velocity V and can only be solved by numerical techniques for the nonsteady conditions of acceleration or deceleration.
Under steady state (constant velocity) the power equation can be written as follows:

The Human Engine

Consider now the human engine. In 1983 Douglas Malewicki gave a landmark paper at the International Human Powered Vehicle Association Scientific Symposium, in which he presented a graph showing the maximum duration of human effort for various steady power levels. This graph has been reproduced below for convenience. Notice from the graph that an average "healthy human" can produce a steady 0.1 horsepower for a full eight hour period, while a "first class athlete" can produce 0.4 horsepower for a similar period. Note that each data point on the curves represents an exhausted human. No more power is available without some rest and recovery. Thus at 0.4 hp the "healthy human" becomes exhausted within 10 minutes! Try to decide where you fit in this curve.

Note that in the power equation the units of power is watts (W), however we can apply the conversion 0.1 hp = 75 W (approximately) in reading the graph. Once you have decided the steady power level that you can comfortably apply at the pedals, it would be of interest to know the velocity that you will achieve at steady state when all other parameters are maintained at constant values. Unfortunately the steady state power equation above cannot be solved explicitly for velocity, thus we will develop a root finding technique to solve this problem in a forthcoming exercise. This first exercise introduces modular programming using functions, and is much less ambitious:

The Computer Program

There are two parts to this exercise, the computer program to evaluate the applied power as a function of velocity, and a graph which you will plot by hand on regular graph paper.

Notice that in this exercise we have used the computer in a very unsophisticated role - as a mere calculator. In the coming exercises we will successively (and joyfully) relinquish all of the manual processes above (multiple execution of the program, drawing the graph, determining the steady state velocity for a specified applied power) to the computer.